Conchas de Chocolate

Name: Conchas de Chocolate
Cuisine: Mexican
Ingredients: 1 ¼-oz. envelope active dry yeast (about 2¼ tsp.); ½ cup warm whole milk (about 110°); 3 large eggs, room temperature; 6 Tbsp. (75 g) granulated sugar; 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt; 3 Tbsp. nonfat dry milk powder; 3 cups (375 g) bread flour, plus more for surface; 10 Tbsp. unsalted butter, cut into 10 even pieces, room temperature; 1 cup plus 1 Tbsp. (133 g) all-purpose flour; ⅔ cup (73 g) powdered sugar; ½ cup ghee, refined coconut oil, or vegetable shortening, melted and cooled; 2 Tbsp. unsweetened cocoa powder, preferably Dutch-process; 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt; 1 tsp. vanilla paste or extract; 1 large egg